Algebraic Modeling
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Graphing Data
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Analyzing Data
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Solving Problems Algebraically and Graphically
Functions Defined and Notation
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Domain
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Range
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Boundedness
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Local and Absolute Extrema
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Symmetry
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Asymptotes
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End Behavior
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Introduction to Twelve Basic Functions
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Function Composition
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Modeling with Functions
Linear and Quadratic Functions
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Linear Functions and Graphs
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Average Rate of Change
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Linear Correlation and Modeling
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Graphing Quadratic Functions
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Applications of Quadratic Functions
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Linear and Quadratic Functions on a Graphing Calculator
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Completing the Square
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The Quadratic Formula
Power Functions and Variation
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Graphing Power Functions
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Modeling with Power Functions
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Power Functions and Variation on a Graphing Calculator
Polynomial Functions of Higher Degree
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Graphing Polynomial Functions
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End Behavior
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Zeros
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Intermediate Value Theorem
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Polynomial Functions of Higher Degree on a Graphing Calculator
Real Zeros of Polynomials
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Zero Factor Property
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Long Division of Polynomials
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Remainder and Factor Theorems
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Synthetic Division
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Rational Zeros
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Upper and Lower Bounds
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Real Zeros of Polynomials on a Graphing Calculator
Complex Zeros
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Fundamental Theorem of Algebra
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Complex Conjugate Zeros
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Factoring Real Number Coefficients
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Complex Zeros on a Graphing Calculator
Graphing Rational Functions
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Transformations of the Reciprocal Function
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Limits - End Behavior and Asymptotes
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Graphing Rational Functions on a Graphing Calculator
Solving Rational Equations
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Extraneous Solutions
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Solving Rational Equations on a Graphing Calculator
Solving Rational Inequalities
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Sign Charts
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Polynomial Inequalities
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Solving Rational Inequalities on a Graphing Calculator
Exponential and Logistic Functions
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Exponential and Logistic Graphs
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The Natural Base e
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Population Models
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Exponential and Logistic Functions on a Graphing Calculator
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Scientific Notation
Exponential and Logistic Modeling
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Constant Percentage and Exponentials
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Exponential Growth and Decay
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Modeling Population with Regression on a Graphing Calculator
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Other Logistic Models
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Exponential and Logistic Modeling on a Graphing Calculator
Properties of Logarithmic Functions
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Logarithm-- Inverse of an Exponential Function
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Common Logs
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Functions with Base b
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Natural Logs
Solving Exponential and Logarithmic Equations
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Orders of Magnitude
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Logarithmic Models
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Newton's Law of Cooling
Vectors in the Plane
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2-D Vectors
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Vector Operations
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Unit Vectors
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Direction Angles
Dot Product of Vectors
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The Dot Product
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Angle between Vectors
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Vector Projection
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Work
Polar Coordinates
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The Polar Coordinate System
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Converting Coordinates from Rectangular to Polar
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Converting Coordinates from Polar to Rectangular
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Converting Equations from Polar to Rectangular
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Finding Distance Between Polar Coordinates
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Rose Curves
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Cardioid Curves
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Limacon Curves
Complex Numbers in Trigonometric Form
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Complex Number Plane
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Trigonometric Form of Complex Numbers
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Multiplication of Complex Numbers
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Division of Complex Numbers
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Powers of Complex Numbers
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Roots of Complex Numbers
Solving Systems of Two Equations
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Solving by Substitution
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Solving by Elimination
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Solving Graphically
Matrix Algebra
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Addition of Matrices
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Subtraction of Matrices
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Multiplication of Matrices
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Identity Matrix
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Inverse Matrix
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Determinant of a Square Matrix
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Cramer's Rule
Matrix Row Operations
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Gaussian Elimination
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Elementary Row Operations
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Reduced Row Echelon Form
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Solving a System of Equations Using a Matrix
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Partial Fraction Decomposition (Linear Denominators)
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Partial Fraction Decomposition (Irreducible Quadratic Denominators)
Systems of Inequalities in Two Variables
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Graphing Systems of Inequalities
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Linear Programming
Geometry of a Parabola
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Standard Form of the Equation
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Vertex Form of the Equation
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Identify Critical Points
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Graphing Parabolas
Geometry of an Ellipse
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Standard Form of the Equation
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General Form of the Equation
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Identify Critical Points
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Graphing Ellipses
Geometry of a Hyperbola
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Standard Form of the Equation
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General Form of the Equation
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Identify Critical Points
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Graphing Hyperbolas
Translation and Rotation of Axis
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Graphing Conic Sections Algebraically
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Graphing Conic Sections on a Graphing Calculator
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Translation of a Conic Section
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Rotation of a Conic Section
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Finding the Angle of Rotation
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Finding the Coefficients for a Conic in a Rotated System
Polar Equations of Conic Sections
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Writing Polar Equations for Conic Sections
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Analyzing Polar Equations for Conic Sections
3-D Cartesian Coordinate System
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3-D Coordinates
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Finding Distance and Midpoint
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Equation of a Sphere
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Planes
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Vectors in Space
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Lines in Space
The Binomial Theorem
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Powers of the Binomial
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Pascal's Triangle and Binomial Expansion
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The Binomial Theorem
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Factorial Identities
Sequences
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Infinite Sequences
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Limits of Infinite Sequences
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Arithmetic Sequences
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Geometric Sequences
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Working with Sequences on a Graphing Calculator
Series
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Summation Notation
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Sums of Arithmetic Sequences
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Sums of Geometric Sequences
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Infinite Series
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Convergence of Geometric Series
Limits, Motion, and the Tangent Line
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Average Velocity
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Instantaneous Velocity
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The Derivative by Definition
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Definition of the Tangent Line
Limits, Motion, and Areas
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Distance from a Constant Velocity
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Distance from a Changing Velocity
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Connection to Areas
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The Definite Integral
Limits
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Concepts and Informal Definition of a Limit
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Properties of Limits
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Limits of Continuous Functions
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One-Sided Limits
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Two-Sided Limits
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Limits Involving Infinity
Graphs of Trigonometric Functions
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Graphing Trigonometric Functions with Domain and Range
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Graphing Trigonometric Functions with Critical Points
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Graphing Trigonometric Functions with Translations and Asymptotes
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Graphing Sine and Cosine
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Translations of Sinusodial Graphs
Uncategorized Questions
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A piece of wire 40 cm long is cut into two square pieces. If the side length of one of the squares is x cm, what is the side length of the other square?
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Question #46b17
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What is #(2^(x+4) - 2(2^x))/(2*(2^(x+3))#?
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What is the explicit formula in "29, 229, 429, 629..."?
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It takes Zoe 12.5 minutes to swim 20 laps around the pool. What is Zoe’s unit rate?
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What is #(sqrt7^((log_7)400))#?
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What is the vertex of the function #p(x) = (x-5)^2 + 4#?
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What is the 10th term of the sequence "12, 23, 34, 45...."? How do you write an equation for the #n#th term of the sequence?
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How do you express #4x i+5yi^8+6x i^3+2yi^4# in simplest #a + bi# form?
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What are the next two terms in the pattern 3, 6, 5, 10,9, 18, 17, . . .?
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What is the end behavior of the graph of #y = 2x^3 + 5x#?
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What is the value of the polynomial #-6x^2-3y^2+6xy-5#, given #x = .9# and #y = -6.7#?
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Conics Question:
Graph the equation
x=-3y^2+12y+13
What are all applicable points? (vertex, focus, etc.)
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What's the equation of the circle?
The end points of the diameter (4,8) and (8,-10)
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Graph the equation.
#(3x^2)-(2y^2)-9x+4y-8=0#
What are all applicable points (vertex, focus, center, etc)?
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Solve for x and y?
xy-x^2= -20
x-2y=3
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What is #x# in the equation #Exp_b[log_b(2x)] = ln(e^(54-4x))#?
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What is b in the equation: #Exp_b(3) = 27#?
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How do you convert #(-sqrt 3, -1) # into polar coordinates?
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Question #ea843
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Is the sequence "7, 17, 27, 37..." arithmetic? If so, what is the formula?
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Is the sequence "7, 3, 13, 23,..." arithmetic? If so, what is the explicit formula?
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Is the sequence "#4, 16, 36, 64,...#" arithmetic?
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Let #f(x) =-2x+7# and #g(x) = -6x+3#. What is #f *g# and what is its domain?
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How do you rewrite #f(x) = x^2 - 8x + 12# in standard form #f(x) = (x-h)^2 + k#?
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What is the inverse of the function #f(x) = -3x + 3#?
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What is the equation for a parabola in vertex form?
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Let #f(x)= -4x + 7# and #g(x)= 10x-6#. What is #f(g(x))#?
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Given that #(a+b)^2 = 189# and #6ab = 78#, what is the value of #3(a^2+b^2)#?
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How to use the price demand equation : x = f(p) = 60,000 - 700p to find E(p), the elasticity of demand?
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What is the range of #f(x) = -4x + 5# for the domain #{-3, -1, 0, 3}#?
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The point A is on the positive y-axis and B is on the positive x-axis. P lies on AB such that AP=36 and BP=9. What is the equation of the loci of P?
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Question #89327
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What is the quotient and the remainder when #x^4 — 2x^2 +3x - 1# is divided by #x+1#?
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What is #(5!3!)/(6!)#?
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What is #(1 + i)^8# in rectangular form?
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How many terms of the arithmetic sequence #{1,3,5,7,...}# will give a sum of #961#?
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The 10th term of an arithmetic sequence is 10 and the sum of the first 10 terms is -35. What is the first term and the common difference of the sequence?
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Question #589e3
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Question #35b7d
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What are the next two terms of the sequence: #4, -20, 100, -500#?
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Question #3c26f
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What are the asymptotes and removable discontinuities, if any, of #f(x)= (3x)^2/(x^2-x-6)+3 #?
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What are the asymptotes and removable discontinuities, if any, of #f(x)=6/x-2#?
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A daily newspaper had 12,125 subscribers when it began publication. Five years later it had 10,100 subscribers. What is the average yearly rate of change in the number of subscribers for the five-year period?
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How do you divide #5x^2 - 6x^3 + 1 + 7x# by #3x - 4#?
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How do you use synthetic division to divide #x^3+7x^2-12x-10# by #x+1#?
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What is the rule of the sequence #1.5, 3.9, 6.3, 8.7 ...#?
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A certain bacterium can divide every 30 min. If you begin with 1 bacterium, when will you have more than 1,000 bacteria?
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Question #16c31
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What is the solution to the quadratic inequality #2x^2-6x>=5#?
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The vertex of a parabola is #(1, 3)# and another point on the parabola is #(- 1, - 1)#. What is another point also on the parabola?
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How do you solve the logarithmic equation #ln(x) + ln(x - 1) = ln2#?
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What is the pattern in the sequence, #28, -2, -32, -62#?
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What is #x# in the equation #log_3x^2 - log_"5"25 = log_"2"16#?
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What is #(7+4i)/(6-8i)#?
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What is #root(3) 1000#?
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Given #f(x)=-5x^4 + 4x^3 - 7x^2 - 6x - 3#, what is #f(-3)#?
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Given #f(x)= 5x-4# and #g(x)=7x + 6#, what is #g(f(x))#?
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Question #08c9e
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How do you use Pascal's Triangle to expand #(x - 2)^4#?
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In 1998 the enrollment at a community college was approximately 2500 students. In 2002 the enrollment had increased to 3250 students. If the enrollment continues to increase at this rate, what is a reasonable projection of enrollment for 2010?
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What is #i^1234# equivalent to?
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How do you simplify #6!#?
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What is the 12th term of the sequence #4, 12, 36# and what is the sum of all 12 terms?
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How do you solve #z( 3 + 2i) = (2 — 3i)#?
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How do you solve #x^(2/3) - 3x^(1/3) - 4 = 0#?
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How do you solve #|9 - 3g| <= 12#?
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How many solutions does the system of equations #3x + 7y = 4# and #6x + 14y = 8# have?
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Solve the equation #3*2^x=24#?
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What are all the rational zeroes of #f(x) = x^3 - 3x^2 - 4x + 12#?
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Is the function #f(x) = 5 * x^-5# a monomial function?
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What is the value of #x# in #log(5) = 2 - log(x)#?
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How do you solve the linear system #y = -1/2x + 2# and #y = 3x -5#?
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The product of #(root5 8)##(root3 16)# can be expressed as #2^n#. What is the value of #n#?
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What is #x# in the equation #ln((x-2)^2) = 14#?
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The roots of #x^2 + 2x + c = 0# differ by #4i#. What are the roots, and what is the value of #c#?
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How do you solve #y > sqrt(x + 3)#?
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What is the degree of the function #f(x) = x^4 - 12x^3 + 5x^2 - 9#?
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In what quadrant does the point #(7.9, -24.6)# lie?
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What is #f^-1(3)# when #f(x) = (2x + 3) / 5#?
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Question #644fe
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What is the domain of #g(x) = sqrt(-3x - 2)#?
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Question #6ab46
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What is the horizontal asymptote of #f(x) = (-5x)/(sqrt(16x^2 + 7))#?
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Thorsten the geologist is in the desert, 10 km from a long, straight road. On the road, Thorsten's jeep can do 50kph, but in the desert sands, it can manage only 30kph. How many minutes will it take Thorsten to drive through the desert? (See details).
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How do you solve #2^(x+4) = 3^(2x+1)# ?
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How do you solve #log_2x + log_2(x+2) = 3#?
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What is the partial fraction decomposition of #f(x) = (-7x + 15)/(x^2 + 5x)#?
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How do you solve #81^x = 9(3^x)#?
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How many solutions are there to the system of equations #y + x = 3# and #6 = 2x - y#?
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In an arithmetic sequence, #f(0) = 8# and #f(2) = 12. What are the first several terms of the sequence?
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What is the explicit formula of 15, 10, 5, 0, -5, -10,...?
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What is a quadratic function with a maximum at #(3, 125)# and roots at #-2# and #8#?
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If #f(x) = -2x^2 + 2x -2#. what is #f(a-1)#?
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If #x=4i# is a root of #f(x) = x^4 - 4x^3 +29x^2 -64x + 208# what are the other roots?
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How do you convert #(3sqrt3, - 3)# from rectangular coordinates to polar coordinates?
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How do you write the partial fraction decomposition of the rational expression # (3x + 2) / [(x - 1)(x + 4)]#?
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How do you write the partial fraction decomposition of the rational expression #x^3/(x^2 + 4x + 3) #?
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How do you write the partial fraction decomposition of the rational expression #( 2x + 1)/( (x+1)^3 (x^2+4)^2 )#?